Mathematics K–11

The Pearson System of Courses for mathematics provides an innovative, engaging curriculum beginning in kindergarten and extending through Grade 11—a system designed from the ground up to help students achieve the goals of the Common Core State Standards (CCSS) for Mathematics.

Each course provides a full school year of instruction, comprising a series of related units. Students explore three different unit types—Concept Units, Modeling Units, and Project Units—during the school year. Together, these units give students an in-depth understanding of key mathematical concepts, engage students in sustained mathematical problems, and provide real-world challenges to which students can immediately apply all they have learned.

Concept Units

Concept Units give students an in-depth understanding of one or more mathematical concepts delineated by the CCSS for Mathematics.

Students develop this understanding through independent exploration and guided instruction. They engage with targeted problems—independently, in small groups, and with the whole class. This classroom routine makes it possible for students to give and receive feedback, to check their work, and to critique the work of others.

Modeling Units

Modeling Units encourage students to collaborate to put the math they have learned to work.

Students work together to explore two to five related tasks over the course of 1–3 days. These tasks, which integrate recently introduced or reviewed mathematical concepts, are based on standards from at least two different domains; in some cases as many as five different domains are used. Then, students are encouraged to turn their focus to greater mastery of a single concept in the mathematics Gallery. In the Gallery, students can put the mathematics to work by solving problems they choose themselves or by attempting problems suggested directly to them by their teacher.

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Project Units

Project Units encourage students to apply the mathematics they have learned to a large-scale piece of real-world work based on one or more concepts.

Students are encouraged to choose the projects they work on, which can take the form of written work, models, video, online slideshows, and so on. Some projects ask students to apply their knowledge to a single concept; e.g., producing a scale model of an object by using ratios. Students also have the opportunity to explore multiple-concept projects—endeavors such as designing a physical structure, carrying out a study of a prospective business, and collecting and analyzing data related to a current economic or social issue.

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The Mathematics Lesson

The lesson is the fundamental structure for learning and instruction within the Pearson System of Courses for mathematics.

Lessons within each unit focus students on developing skills and knowledge that deliberately build upon previously learned skills and practices. Within each unit, carefully sequenced sets of lessons fully address the Common Core State Standards.

From kindergarten onward, the Pearson System of Courses organizes students’ learning of mathematics around proven activities and routines consistently presented. These experiences include repeated routines in the lesson such as the Opening, Work Time, Ways of Thinking, Apply the Learning, Summary of the Math, and Reflection. 

These routines collectively give students an in-depth understanding of the mathematical concepts targeted by the Common Core State Standards for Mathematics. As these behaviors become habits for students, teachers have the chance to spend less time on managing the classroom and more time on teaching.

Follow the tabs below to review representative routines from the third grade unit “Divide.” A Getting Started screen, like the one to the right, provides students and teachers immediate access to each of the lessons in the unit and, in the text at the top of the left-hand column, offers a quick overview of unit goals and learning objectives.

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Mathematics Grades 2–11 Lesson

Opening

Each lesson in the Pearson System of Courses for mathematics begins with an Opening that sets the stage for the lesson.

The lesson Opening is a brief, teacher-directed session in which students learn about the problem or concept they will be working on. The Opening may pose a question or ask students to make a prediction about a concept or problem that will be the focus of study. Typically, this investigation is prompted by an invitation to watch a video, review a text, explore a digital interactive, or get ready for a teacher demonstration or discussion that announces the lesson objectives. 

In addition to giving students an understanding of what they are expected to learn, the lesson Opening prepares students for the next routine: Work Time.

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This lesson Opening asks students to watch the video in which 4 children share 12 strawberries and then answer questions about what they observed.

Work Time

During Work Time, students work on a problem or series of mathematical problems independently or with partners, and then share and discuss their work.

Once the challenges of the lesson have been framed by the Opening, students work independently, with partners, or both on a problem or series of mathematical problems. They then share and discuss their work.

Work Time gives students the opportunity to engage with rigorous mathematics independent of the teacher. This routine invites mathematical exploration during which students first develop their own ideas and responses to a challenging problem. Next, they refine their understanding by working with a partner. Finally, they share what they know and learn from others within their class.

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Now that students have watched the video, students move on to Work Time. In this task, students use an interactive to divide the strawberries equally. Interactives are an important element of helping students to engage with the math lessons more deeply.

Interactives

Many Work Time explorations ask students to explore and respond to digital interactives that make it easy to immediately apply and model a specific mathematical concept. 

These digital games and investigations serve as springboards to many mathematical concepts presented throughout the larger unit of study. Each interactive records students’ work and saves the result so that it may be returned to as often as needed. Students can even share their progress via their Notebook so that others can learn from their achievement.

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Here the student has begun the process of modeling the problem by dragging the strawberries to buckets.

Prepare a Presentation

In addition to exploring concepts by working with interactives during Work Time, students are often asked to prepare a presentation that demonstrates how they would approach and solve a particular mathematical problem.

To develop their ideas—and share their conclusions—students can access their very own personal Notebook at any time during a lesson. Within their personal Notebook, they can easily draw, write, or type their answers to a problem. Everything entered in the Notebook is saved until erased. Students can share the contents of their Notebook at any time with their teacher, classmates, or the entire class.

For more information on the many ways students can use the Notebook, refer to System Overview—Using the Notebook.

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Here, students can draw diagrams, create graphs, and explain how they solved a given problem. Students who finish early can tackle a Challenge Problem.

Ways of Thinking

During Ways of Thinking, students share and explain their work.

The term “Ways of Thinking” is taken from Japanese and Singaporean instruction and refers to the way that a student thinks about a task. The essence of Ways of Thinking is the discussion, during which students focus on the mathematical concepts of the lesson, strive to clearly explain their work, and consider alternative approaches to solving problems.

This routine allows students to listen to the reasoning of others and to be introduced to and understand the multiple ways one can access mathematical knowledge. Ways of Thinking also provides teachers with an important personalization strategy, allowing individuals or groups of students to work at their own pace to develop an approach that makes sense to them.

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While listening to their classmates share and explain their work, students take notes to help them gain a deeper understanding of the mathematical concept and the multiple ways a problem can be solved.

Apply the Learning

After students have had a chance to consider different ways of approaching the same mathematical problem, they can immediately apply what they’ve considered during a routine developed expressly to encourage this application.

When students Apply the Learning, they are challenged to approach problems similar to those they tackled during Work Time. Applying different ways of thinking to similar problems helps them see how specific concepts can be applied to a variety of mathematical challenges.

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Now that students have a foundational understanding of the strawberry problem as an equation using multiplication, this concept is then related to division—the main idea in this unit. The tasks in the rest of the lesson (not shown here) present students with division problems that gradually increase in difficulty.

Summary of the Math

Students begin their concluding activities for the lesson during the routine called Summary of the Math. During this activity, they have the chance to summarize and consolidate their understanding of the mathematical concepts to which they’ve been introduced. To do so, they generally work independently to solve a representative problem from the lesson and then share their approach with others in a teacher-led discussion.

This group activity helps students share what they’ve learned with others—and provides a chance to learn from their peers. At the same time, Summary of the Math gives teachers the opportunity to review the content being learned, quote student work, and quickly assess student understanding.  

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During this Summary of the Math, students review how the answer to a division problem can be found by using multiplication.

Reflection

Following Summary of the Math, students are asked to write a brief Reflection about the day’s learning.

This concluding routine asks students to write a personal statement articulating what they have learned from a lesson. They can choose to write their personal Reflection based on their own ideas or in response to a given writing prompt. Students may also use their Reflection as an opportunity to record or resolve questions.

Teachers can use the Reflection as an informal assessment of students’ levels of understanding. They can also review these writings to learn more about the types of questions students still have about the mathematical concepts and tasks presented in the lesson.

Once finished with the lesson, students can visit the Concept Corner to explore additional tutorials, exercises, and games linked directly to the unit of study.

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Using the Notebook, students write a Reflection about the ideas discussed in class that day.

Concept Corner

Concept Corner makes it possible for teachers and students to explore additional written explanations, videos, and sample problems that correspond with the key mathematical concepts that shape their classroom work.

For mathematics, Concept Corner includes:

Concept Explanations, which present and illustrate specific math concepts addressed in classroom lessons through dynamic videos and written text.

A Glossary, which compiles illustrated, easy-to-understand definitions of math terms, presented by grade level. 

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